#### Submission Type

Presentation

#### Submission Title

An Application of Machine Learning To Protect Against Sure Loss in Games of Chance

#### Session Title

Session 1-4-D: Game Math and a Legacy

#### Location

Caesars Palace, Las Vegas, Nevada

#### Start Date

28-5-2019 3:30 PM

#### End Date

28-5-2019 4:55 PM

#### Disciplines

Applied Statistics | Discrete Mathematics and Combinatorics | Logic and Foundations | Probability | Statistical Theory

#### Abstract

We present novel techniques for protecting players of games of chance from sure loss. Since Ramsey (1926) decision theorists have known that players whose betting positions violate the laws of probability expose themselves to arbitrage. We regard such violations as simple mathematical errors to be rectified. No known techniques for correcting broken betting positions have been developed, so we introduce a technique. Given an incoherent set of bets, we characterize nearby coherent sets of bets and provide algorithms to compute them. Bets are compared using the L2-loss function commonly employed in linear regression. A machine learning algorithm based on AdaBoost from Freund et al. (1997) is presented which compute the closest consistent set of bets to a flawed set. We prove a lower bound on the worst case convergence rate of the algorithm introduced. We show how to use machine learned bets as the basis for other bets without fear of arbitrage. The tools developed are new defenses against costly mathematical errors. While the techniques developed here are suited to games of chance, they provide a non-parametric framework for machine learning any joint probability distribution from specified training data.

The algorithms presented provide a novel safeguard to protect gamblers from exploitation.

#### Keywords

Machine Learning, Probability, Gambling, Arbitrage, Regression, L2-Loss

#### Funding Sources

Corporate funding

#### Competing Interests

None

An Application of Machine Learning To Protect Against Sure Loss in Games of Chance

Caesars Palace, Las Vegas, Nevada

We present novel techniques for protecting players of games of chance from sure loss. Since Ramsey (1926) decision theorists have known that players whose betting positions violate the laws of probability expose themselves to arbitrage. We regard such violations as simple mathematical errors to be rectified. No known techniques for correcting broken betting positions have been developed, so we introduce a technique. Given an incoherent set of bets, we characterize nearby coherent sets of bets and provide algorithms to compute them. Bets are compared using the L2-loss function commonly employed in linear regression. A machine learning algorithm based on AdaBoost from Freund et al. (1997) is presented which compute the closest consistent set of bets to a flawed set. We prove a lower bound on the worst case convergence rate of the algorithm introduced. We show how to use machine learned bets as the basis for other bets without fear of arbitrage. The tools developed are new defenses against costly mathematical errors. While the techniques developed here are suited to games of chance, they provide a non-parametric framework for machine learning any joint probability distribution from specified training data.

The algorithms presented provide a novel safeguard to protect gamblers from exploitation.

## Comments

This is my abstract only.

My brief abstract is as follows:

We present a novel technique for protecting players of games from sure loss. Betting positions which violate the laws of probability are open to arbitrage. Given such a set of bets, we provide an algorithm for correcting them using machine learning. The result protects against exploitation due to mathematical error.